{"id":120743,"date":"2026-11-01T07:40:39","date_gmt":"2026-10-31T23:40:39","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/120743.html"},"modified":"2026-11-01T07:40:39","modified_gmt":"2026-10-31T23:40:39","slug":"c%e4%bb%a3%e7%a0%81%e5%ae%9e%e7%8e%b0matlab%e4%b8%ad%e7%9a%84shapley%e5%87%bd%e6%95%b0%e5%8a%9f%e8%83%bd","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/120743.html","title":{"rendered":"C++\u4ee3\u7801\u5b9e\u73b0MATLAB\u4e2d\u7684shapley\u51fd\u6570\u529f\u80fd"},"content":{"rendered":"

\/\/ shapley.cpp<\/span>
\n\/\/ \u6574\u5408：\u901a\u7528\u7279\u5f81\u51fd\u6570 Shapley + MATLAB \u98ce\u683c\u5305\u88c5 + \u52a0\u6743\u591a\u6570\u535a\u5f08 Shapley-Shubik<\/span>
\n#<\/span>include<\/span> <vector><\/span><\/span>
\n#<\/span>include<\/span> <cmath><\/span><\/span>
\n#<\/span>include<\/span> <iostream><\/span><\/span>
\n#<\/span>include<\/span> <numeric><\/span><\/span>
\n#<\/span>include<\/span> <stdexcept><\/span><\/span>
\n#<\/span>include<\/span> <iomanip><\/span><\/span><\/p>\n

\/\/ ==================== \u5de5\u5177\u51fd\u6570：\u624b\u5199 popcount（\u53ef\u79fb\u690d） ====================<\/span>
\nstatic<\/span> int<\/span> popcount32<\/span>(<\/span>unsigned<\/span> int<\/span> x)<\/span> {<\/span>
\n int<\/span> c =<\/span> 0<\/span>;<\/span>
\n while<\/span> (<\/span>x)<\/span> {<\/span> x &=<\/span> x –<\/span> 1<\/span>;<\/span> ++<\/span>c;<\/span> }<\/span>
\n return<\/span> c;<\/span>
\n}<\/span><\/p>\n

\/\/ ==================== 1. \u901a\u7528\u7279\u5f81\u51fd\u6570 Shapley \u8ba1\u7b97 ====================<\/span>
\n\/\/ \u8f93\u5165: v: \u957f\u5ea6\u4e3a 2^n \u7684\u6570\u7ec4, v[mask] \u8868\u793a\u8054\u76df mask \u7684\u4ef7\u503c<\/span>
\n\/\/ (mask \u7684\u7b2c i \u4f4d\u4e3a 1 \u8868\u793a\u5305\u542b\u73a9\u5bb6 i，\u4ece 0 \u5f00\u59cb\u7f16\u53f7)<\/span>
\n\/\/ \u8f93\u51fa: \u957f\u5ea6\u4e3a n \u7684 Shapley \u503c\u5411\u91cf<\/span>
\nstd::<\/span>vector<<\/span>double<\/span>><\/span> computeShapley<\/span>(<\/span>const<\/span> std::<\/span>vector<<\/span>double<\/span>><\/span>&<\/span> v)<\/span> {<\/span>
\n int<\/span> n =<\/span> 0<\/span>;<\/span>
\n while<\/span> (<\/span>(<\/span>1u<\/span> <<<\/span> n)<\/span> <<\/span> v.<\/span>size<\/span>(<\/span>)<\/span>)<\/span> ++<\/span>n;<\/span>
\n if<\/span> (<\/span>(<\/span>1u<\/span> <<<\/span> n)<\/span> !=<\/span> v.<\/span>size<\/span>(<\/span>)<\/span>)<\/span>
\n throw<\/span> std::<\/span>invalid_argument<\/span>(<\/span>"v.size() must be 2^n"<\/span>)<\/span>;<\/span><\/p>\n

std::<\/span>vector<<\/span>double<\/span>><\/span> phi<\/span>(<\/span>n,<\/span> 0.0<\/span>)<\/span>;<\/span><\/p>\n

\/\/ \u9884\u8ba1\u7b97\u9636\u4e58<\/span>
\n std::<\/span>vector<<\/span>double<\/span>><\/span> fact<\/span>(<\/span>n +<\/span> 1<\/span>,<\/span> 1.0<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span> i =<\/span> 1<\/span>;<\/span> i <=<\/span> n;<\/span> ++<\/span>i)<\/span> fact[<\/span>i]<\/span> =<\/span> fact[<\/span>i –<\/span> 1<\/span>]<\/span> *<\/span> i;<\/span>
\n double<\/span> n_fact =<\/span> fact[<\/span>n]<\/span>;<\/span><\/p>\n

for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> n;<\/span> ++<\/span>i)<\/span> {<\/span>
\n double<\/span> sum =<\/span> 0.0<\/span>;<\/span>
\n int<\/span> mask_i =<\/span> 1<\/span> <<<\/span> i;<\/span><\/p>\n

\/\/ \u679a\u4e3e\u6240\u6709\u4e0d\u5305\u542b\u73a9\u5bb6 i \u7684\u8054\u76df S<\/span>
\n for<\/span> (<\/span>int<\/span> S =<\/span> 0<\/span>;<\/span> S <<\/span> (<\/span>1<\/span> <<<\/span> n)<\/span>;<\/span> ++<\/span>S)<\/span> {<\/span>
\n if<\/span> (<\/span>S &<\/span> mask_i)<\/span> continue<\/span>;<\/span>
\n int<\/span> s =<\/span> popcount32<\/span>(<\/span>(<\/span>unsigned<\/span>)<\/span>S)<\/span>;<\/span>
\n int<\/span> S_with_i =<\/span> S |<\/span> mask_i;<\/span><\/p>\n

double<\/span> marginal =<\/span> v[<\/span>S_with_i]<\/span> –<\/span> v[<\/span>S]<\/span>;<\/span>
\n double<\/span> weight =<\/span> fact[<\/span>s]<\/span> *<\/span> fact[<\/span>n –<\/span> s –<\/span> 1<\/span>]<\/span> \/<\/span> n_fact;<\/span>
\n sum +=<\/span> weight *<\/span> marginal;<\/span>
\n }<\/span>
\n phi[<\/span>i]<\/span> =<\/span> sum;<\/span>
\n }<\/span>
\n return<\/span> phi;<\/span>
\n}<\/span><\/p>\n

\/\/ ==================== 2. MATLAB \u98ce\u683c\u5305\u88c5 ====================<\/span>
\n\/\/ \u8f93\u5165: v \u957f\u5ea6 2^n – 1，\u6309\u4e8c\u8fdb\u5236\u6570\u987a\u5e8f\u5b58\u653e\u975e\u7a7a\u8054\u76df\u4ef7\u503c<\/span>
\n\/\/ （\u4e0e MATLAB shapley(v) \u7684 'right' \u7ea6\u5b9a\u4e00\u81f4）<\/span>
\nstd::<\/span>vector<<\/span>double<\/span>><\/span> shapleyMatlabStyle<\/span>(<\/span>const<\/span> std::<\/span>vector<<\/span>double<\/span>><\/span>&<\/span> v)<\/span> {<\/span>
\n int<\/span> n =<\/span> 0<\/span>;<\/span>
\n while<\/span> (<\/span>(<\/span>1u<\/span> <<<\/span> n)<\/span> –<\/span> 1<\/span> <<\/span> v.<\/span>size<\/span>(<\/span>)<\/span>)<\/span> ++<\/span>n;<\/span>
\n std::<\/span>vector<<\/span>double<\/span>><\/span> v_full<\/span>(<\/span>1u<\/span> <<<\/span> n,<\/span> 0.0<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>size_t mask =<\/span> 1<\/span>;<\/span> mask <<\/span> (<\/span>1u<\/span> <<<\/span> n)<\/span>;<\/span> ++<\/span>mask)<\/span> {<\/span>
\n v_full[<\/span>mask]<\/span> =<\/span> v[<\/span>mask –<\/span> 1<\/span>]<\/span>;<\/span>
\n }<\/span>
\n return<\/span> computeShapley<\/span>(<\/span>v_full)<\/span>;<\/span>
\n}<\/span><\/p>\n

\/\/ ==================== 3. \u52a0\u6743\u591a\u6570\u535a\u5f08（Shapley-Shubik \u6307\u6570） ====================<\/span>
\nint<\/span> g_n =<\/span> 0<\/span>;<\/span>
\nint<\/span> g_quota =<\/span> 0<\/span>;<\/span>
\nstd::<\/span>vector<<\/span>int<\/span>><\/span> g_weights;<\/span>
\nstd::<\/span>vector<<\/span>bool<\/span>><\/span> g_used;<\/span>
\nstd::<\/span>vector<<\/span>double<\/span>><\/span> g_power;<\/span>
\nlong<\/span> long<\/span> g_total_permutations =<\/span> 0<\/span>;<\/span><\/p>\n

void<\/span> dfsShapleyShubik<\/span>(<\/span>int<\/span> depth,<\/span> int<\/span> current_weight,<\/span>
\n bool<\/span> pivot_found,<\/span> int<\/span> pivot)<\/span> {<\/span>
\n if<\/span> (<\/span>depth ==<\/span> g_n)<\/span> {<\/span>
\n if<\/span> (<\/span>pivot_found)<\/span> g_power[<\/span>pivot]<\/span> +=<\/span> 1.0<\/span>;<\/span>
\n ++<\/span>g_total_permutations;<\/span>
\n return<\/span>;<\/span>
\n }<\/span>
\n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> g_n;<\/span> ++<\/span>i)<\/span> {<\/span>
\n if<\/span> (<\/span>g_used[<\/span>i]<\/span>)<\/span> continue<\/span>;<\/span>
\n g_used[<\/span>i]<\/span> =<\/span> true<\/span>;<\/span>
\n int<\/span> new_weight =<\/span> current_weight +<\/span> g_weights[<\/span>i]<\/span>;<\/span>
\n if<\/span> (<\/span>!<\/span>pivot_found &&<\/span> new_weight >=<\/span> g_quota)<\/span> {<\/span>
\n dfsShapleyShubik<\/span>(<\/span>depth +<\/span> 1<\/span>,<\/span> new_weight,<\/span> true<\/span>,<\/span> i)<\/span>;<\/span> \/\/ i \u6210\u4e3a\u5173\u952e\u73a9\u5bb6<\/span>
\n }<\/span> else<\/span> {<\/span>
\n dfsShapleyShubik<\/span>(<\/span>depth +<\/span> 1<\/span>,<\/span> new_weight,<\/span> pivot_found,<\/span> pivot)<\/span>;<\/span>
\n }<\/span>
\n g_used[<\/span>i]<\/span> =<\/span> false<\/span>;<\/span>
\n }<\/span>
\n}<\/span><\/p>\n

std::<\/span>vector<<\/span>double<\/span>><\/span> computeShapleyShubik<\/span>(<\/span>const<\/span> std::<\/span>vector<<\/span>int<\/span>><\/span>&<\/span> weights,<\/span> int<\/span> quota)<\/span> {<\/span>
\n g_n =<\/span> (<\/span>int<\/span>)<\/span>weights.<\/span>size<\/span>(<\/span>)<\/span>;<\/span>
\n g_quota =<\/span> quota;<\/span>
\n g_weights =<\/span> weights;<\/span>
\n g_used.<\/span>assign<\/span>(<\/span>g_n,<\/span> false<\/span>)<\/span>;<\/span>
\n g_power.<\/span>assign<\/span>(<\/span>g_n,<\/span> 0.0<\/span>)<\/span>;<\/span>
\n g_total_permutations =<\/span> 0<\/span>;<\/span><\/p>\n

dfsShapleyShubik<\/span>(<\/span>0<\/span>,<\/span> 0<\/span>,<\/span> false<\/span>,<\/span> –<\/span>1<\/span>)<\/span>;<\/span><\/p>\n

if<\/span> (<\/span>g_total_permutations ><\/span> 0<\/span>)<\/span> {<\/span>
\n for<\/span> (<\/span>double<\/span>&<\/span> p :<\/span> g_power)<\/span> p \/=<\/span> (<\/span>double<\/span>)<\/span>g_total_permutations;<\/span>
\n }<\/span>
\n return<\/span> g_power;<\/span>
\n}<\/span><\/p>\n

\/\/ ==================== main：\u4e09\u4e2a Demo ====================<\/span>
\nint<\/span> main<\/span>(<\/span>)<\/span> {<\/span>
\n std::<\/span>cout <<<\/span> std::<\/span>fixed <<<\/span> std::<\/span>setprecision<\/span>(<\/span>6<\/span>)<\/span>;<\/span><\/p>\n

\/\/ —- \u6f14\u793a 1：\u901a\u7528\u5408\u4f5c\u535a\u5f08 —-<\/span>
\n \/\/ \u73a9\u5bb6\u4f4d\u6620\u5c04：bit0=\u73a9\u5bb61, bit1=\u73a9\u5bb62, bit2=\u73a9\u5bb63<\/span>
\n \/\/ v(\u2205)=0, v({1})=0, v({2})=0, v({1,2})=1, v({3})=0,<\/span>
\n \/\/ v({1,3})=1, v({2,3})=0, v({1,2,3})=1<\/span>
\n std::<\/span>vector<<\/span>double<\/span>><\/span> v =<\/span> {<\/span>0<\/span>,<\/span> 0<\/span>,<\/span> 0<\/span>,<\/span> 1<\/span>,<\/span> 0<\/span>,<\/span> 1<\/span>,<\/span> 0<\/span>,<\/span> 1<\/span>}<\/span>;<\/span>
\n auto<\/span> phi =<\/span> computeShapley<\/span>(<\/span>v)<\/span>;<\/span>
\n std::<\/span>cout <<<\/span> "=== Demo 1: General Coalition Game ===\\\\n"<\/span>;<\/span>
\n std::<\/span>cout <<<\/span> "phi = ["<\/span>;<\/span>
\n for<\/span> (<\/span>size_t i =<\/span> 0<\/span>;<\/span> i <<\/span> phi.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>i)<\/span>
\n std::<\/span>cout <<<\/span> phi[<\/span>i]<\/span> <<<\/span> (<\/span>i +<\/span> 1<\/span> <<\/span> phi.<\/span>size<\/span>(<\/span>)<\/span> ?<\/span> ", "<\/span> :<\/span> ""<\/span>)<\/span>;<\/span>
\n std::<\/span>cout <<<\/span> "]\\\\n\\\\n"<\/span>;<\/span><\/p>\n

\/\/ —- \u6f14\u793a 2：MATLAB \u98ce\u683c\u8f93\u5165（\u53bb\u6389\u7a7a\u96c6，\u957f\u5ea6 2^n – 1） —-<\/span>
\n std::<\/span>vector<<\/span>double<\/span>><\/span> v_matlab =<\/span> {<\/span>0<\/span>,<\/span> 0<\/span>,<\/span> 1<\/span>,<\/span> 0<\/span>,<\/span> 1<\/span>,<\/span> 0<\/span>,<\/span> 1<\/span>}<\/span>;<\/span> \/\/ \u4e0e Demo 1 \u540c\u4e00\u535a\u5f08<\/span>
\n auto<\/span> phi_m =<\/span> shapleyMatlabStyle<\/span>(<\/span>v_matlab)<\/span>;<\/span>
\n std::<\/span>cout <<<\/span> "=== Demo 2: MATLAB-style Input ===\\\\n"<\/span>;<\/span>
\n std::<\/span>cout <<<\/span> "phi = ["<\/span>;<\/span>
\n for<\/span> (<\/span>size_t i =<\/span> 0<\/span>;<\/span> i <<\/span> phi_m.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>i)<\/span>
\n std::<\/span>cout <<<\/span> phi_m[<\/span>i]<\/span> <<<\/span> (<\/span>i +<\/span> 1<\/span> <<\/span> phi_m.<\/span>size<\/span>(<\/span>)<\/span> ?<\/span> ", "<\/span> :<\/span> ""<\/span>)<\/span>;<\/span>
\n std::<\/span>cout <<<\/span> "]\\\\n\\\\n"<\/span>;<\/span><\/p>\n

\/\/ —- \u6f14\u793a 3：\u52a0\u6743\u591a\u6570\u535a\u5f08（5 \u4eba\u7b80\u5355\u591a\u6570） —-<\/span>
\n std::<\/span>vector<<\/span>int<\/span>><\/span> weights =<\/span> {<\/span>1<\/span>,<\/span> 1<\/span>,<\/span> 1<\/span>,<\/span> 1<\/span>,<\/span> 1<\/span>}<\/span>;<\/span>
\n int<\/span> quota =<\/span> 3<\/span>;<\/span> \/\/ \u8fbe\u5230 3 \u7968\u5373\u83b7\u80dc<\/span>
\n auto<\/span> power =<\/span> computeShapleyShubik<\/span>(<\/span>weights,<\/span> quota)<\/span>;<\/span>
\n std::<\/span>cout <<<\/span> "=== Demo 3: Weighted Majority Game (5 players, simple majority) ===\\\\n"<\/span>;<\/span>
\n std::<\/span>cout <<<\/span> "power = ["<\/span>;<\/span>
\n for<\/span> (<\/span>size_t i =<\/span> 0<\/span>;<\/span> i <<\/span> power.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>i)<\/span>
\n std::<\/span>cout <<<\/span> power[<\/span>i]<\/span> <<<\/span> (<\/span>i +<\/span> 1<\/span> <<\/span> power.<\/span>size<\/span>(<\/span>)<\/span> ?<\/span> ", "<\/span> :<\/span> ""<\/span>)<\/span>;<\/span>
\n std::<\/span>cout <<<\/span> "]\\\\n"<\/span>;<\/span>
\n std::<\/span>cout <<<\/span> "total permutations = "<\/span> <<<\/span> g_total_permutations <<<\/span> "\\\\n"<\/span>;<\/span><\/p>\n

return<\/span> 0<\/span>;<\/span>
\n}<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\/\/ shapley.cpp
\n\/\/ \u6574\u5408：\u901a\u7528\u7279\u5f81\u51fd\u6570 Shapley MATLAB \u98ce\u683c\u5305\u88c5 \u52a0\u6743\u591a\u6570\u535a\u5f08 Shapley-Shubik
\n#include
\n#include
\n#include
\n#include
\n#include
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